Closure systems of equivalence relations and their labeled class geometries

Authors:
Tim B. Kaiser
Affiliations:
Darmstadt University of Technology, Darmstadt, Germany
Venue:
CLA'06 Proceedings of the 4th international conference on Concept lattices and their applications
Year:
2006

Citing 3
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Abstract

The notion of an affine ordered set is specialized to that of a complete affine ordered set, which can be linked to attribute-complete many-valued contexts and is categorically equivalent to the notion of a closed system of equivalence relations (SER). This specialization step enables us to give conditions under which the complete affine ordered set can be interpreted as the set of congruence classes labeled with the congruence relation they stem from yielding a coordinatization theorem for affine ordered sets.